HIGHLY ACCURATE DISCRETE METHODS FOR NONLINEAR PROBLEMS.

Abstract

We study in this work the acceleration of the convergence of discretization algorithms for the solution of nonlinear operator equations in Banach spaces. Two methods, usually used with finite difference schemes, are extended to this general case and their asymptotic properties are established. These are: the Successive Extrapolations method (Richardson's 'extrapolation to the limit', Romberg integration), and the Iterated Deferred Corrections method (Fox's difference correction). The application of these procedures to nonlinear boundary value problems in one and two dimensions is discussed in detail and a complete set of numerical examples is presented. This includes the problem of finding periodic solutions in the case of forced oscillations. (Author)

Document Details

Document Type
Technical Report
Publication Date
May 01, 1967
Accession Number
AD0657576

Entities

People

  • Victor L. Pereyra

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Banach Space
  • Boundaries
  • Boundary Value Problems
  • Convergence
  • Differential Equations
  • Equations
  • Extrapolation
  • Mathematical Analysis
  • Mathematics
  • Oscillation

Fields of Study

  • Mathematics

Readers

  • Fluid Dynamics.
  • Mathematical Modeling and Probability Theory.
  • Operations Research

Technology Areas

  • Space